Integrated Compensation and Rotation Alignment for Three-Axis Magnetic Sensors Array

The differential magnetic gradient tensor system is usually constructed from the three-axis magnetic sensor array, thus making the misalignment error between the sensors become the main source of the measurement error. In addition, the sensor axial biases, scale factors, non-orthogonality, and external magnetic distortion fields severely affect the tensor measurement accuracy simultaneously when the system is applied as a strapdown device. Considering the systematic error and the magnetic interferences, the integrated error coefficient matrix and the integrated bias vector is constructed according to the magnetic field mathematical model of the hard and soft ferromagnetic material, and the integrated compensation model of the sensor is established based on the least-squares (LS) ellipsoid fitting. The rotation matrixes of the roll, pitch and yaw conversion of the sensors are constructed, and the misalignment error calibration model of the sensor array is obtained. The two linear equations that rotate only about one axis are extracted and the misaligned angles are estimated by the LS method to calibrate the tensor system. Simulation and experimental results show that the proposed method compensates the integrated error of magnetic sensor effectively, and requires only a few measurement data to align the sensor array accurately, which efficiently improves the measurement accuracy of the magnetic gradient tensor system.